Solve 81^-frac{3{4}}div49^-frac{1{2}}*(2/3)^-1

$$81 ^ { - \frac { 3 } { 4 } } \div 49 ^ { - \frac { 1 } { 2 } } \times ( \frac { 2 } { 3 } ) ^ { - 1 }$$

Evaluate

$$\frac{7}{18}\approx 0.388888889$$

Solution Steps

Calculate 81 to the power of -\frac{3}{4} and get \frac{1}{27}.

$$\frac{\frac{1}{27}}{49^{-\frac{1}{2}}}\times \left(\frac{2}{3}\right)^{-1}$$

Calculate 49 to the power of -\frac{1}{2} and get \frac{1}{7}.

$$\frac{\frac{1}{27}}{\frac{1}{7}}\times \left(\frac{2}{3}\right)^{-1}$$

Divide \frac{1}{27} by \frac{1}{7} by multiplying \frac{1}{27} by the reciprocal of \frac{1}{7}.

$$\frac{1}{27}\times 7\times \left(\frac{2}{3}\right)^{-1}$$

Multiply \frac{1}{27} and 7 to get \frac{7}{27}.

$$\frac{7}{27}\times \left(\frac{2}{3}\right)^{-1}$$

Calculate \frac{2}{3} to the power of -1 and get \frac{3}{2}.

$$\frac{7}{27}\times \frac{3}{2}$$

Multiply \frac{7}{27} and \frac{3}{2} to get \frac{7}{18}.

$$\frac{7}{18}$$

Factor

$$\frac{7}{2 \cdot 3 ^ {2}} = 0.3888888888888889$$